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# scaling
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Convert quantities between model and prototype scale using Froude and Reynolds similitude.
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## Installation
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```
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pip install git+http://git.wrl.unsw.edu.au:3000/danh/scaling.git
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```
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## Usage
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```python
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>>> from scaling import FroudeConverter
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>>> froude = FroudeConverter()
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>>> # Convert model value of 200 mm to prototype value (m) with scale of 10
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>>> froude.model_to_proto(200, length_scale=10, input_unit='mm', target_unit='m')
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2.0
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>>> # Get Froude scaling exponent for quantities of time
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>>> froude.scaling_exponent('s')
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0.5
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>>> # Get length, mass and time dimensions for quantities of energy
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>>> froude.dimensions('kJ')
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'L^2 M^1 T^-2'
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```
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Dataframes are also accepted, and specific units can be specified for the values in the index.
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```python
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>>> T = 2
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>>> H = 100
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>>> # Generate regular waves with height=100mm, and period=2s
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>>> t = np.arange(0, 10.1, 0.1)
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>>> eta = 0.5 * H * np.sin(t * 2 * np.pi / T)
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>>> df_model = pd.DataFrame(index=t, data=eta)
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>>> df_model.columns = ['$\eta$ (mm)']
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>>> df_model.index.name = 'Time (s)'
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>>> df_model.plot()
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```
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```python
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>>> # Convert to prototype dimensions, with length scale=25
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>>> df_proto = froude.model_to_proto(
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df_model,
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length_scale=25,
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input_unit='mm',
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target_unit='m',
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index_input_unit='s',
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index_target_unit='s')
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>>> df_proto.columns = ['$\eta$ (m)']
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>>> df_proto.plot()
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```
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`scaling` uses `pint` for unit and dimension conversions. `pint` is able to interpret a wide range of different input units.
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```python
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>>> # Convert water head model value (mm) to prototype pressure value (kPa)
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>>> froude.model_to_proto(10, length_scale=100, 'mm.H20', 'kPa')
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9.80665
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>>> # Demonstrate different ways of specifying units of newtons
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>>> froude.dimensions('N')
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'L^1 M^1 T^-2'
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>>> froude.dimensions('newton')
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'L^1 M^1 T^-2'
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>>> froude.dimensions('kg.m/s/s')
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'L^1 M^1 T^-2'
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>>> froude.dimensions('kilogram.metre/second^2')
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'L^1 M^1 T^-2'
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```
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## Froude scaling reference
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| Quantity | Dimensions | Scaling exponent |
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|--------------|---------------|------------------|
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| Length | L^1 | λ^1 |
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| Mass | M^1 | λ^3 |
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| Time | T^1 | λ^0.5 |
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| Velocity | L^1 T^-1 | λ^0.5 |
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| Acceleration | L^1 T^-2 | λ^0 |
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| Force | L^1 M^1 T^-2 | λ^3 |
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| Pressure | L^-1 M^1 T^-2 | λ^1 |
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| Overtopping | L^2 T^-1 | λ^1.5 |
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## Reynolds scaling reference
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| Quantity | Dimensions | Scaling exponent |
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|--------------|---------------|------------------|
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| Length | L^1 | λ^1 |
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| Mass | M^1 | λ^3 |
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| Time | T^1 | λ^2 |
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| Velocity | L^1 T^-1 | λ^-1 |
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| Acceleration | L^1 T^-2 | λ^-3 |
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| Force | L^1 M^1 T^-2 | λ^0 |
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| Pressure | L^-1 M^1 T^-2 | λ^-2 |
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| Overtopping | L^2 T^-1 | λ^0 |
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